Controlled Magnetohydrodynamic Fluidic Networks and Stirrers

ABSTRACT

The present invention relates to controlled, magnetohydrodynamically-driven, fluidic networks containing a plurality of individually controlled branches. The branches consist of conduits equipped with pairs of electrodes that are controlled by electrode controllers. In operation, the network is placed within a magnetic field and potentials or currents are applied across electrode pairs within the various branches of the network in specifically determined magnitudes and polarities for specifically determined time intervals in accordance with an activation sequence that may be determined by an algorithm. Placed within a temperature gradient, at least a part of the network can act as a thermal cycler for use in biological interactions that employ temperature variations. The invention also relates to magnetohydrodynamic stirrers comprising a conduit or cavity having at least two electrodes disposed in such an orientation that, upon the application of a potential or current across the electrode pair within a magnetic field, secondary flows such as chaotic advection is generated.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of pending U.S. patentapplication Ser. No. 12/062,050 filed Apr. 3, 2008, now allowed, whichis a divisional of U.S. Pat. No. 7,371,051 which issued on May 13, 2008and was filed as U.S. patent application Ser. No. 10/657,302 on Sep. 8,2003, which in turn is based on and claims the benefit of U.S.Provisional Patent Application No. 60/409,359, filed Sep. 9, 2002, nowexpired, all of which are incorporated herein by reference.

GOVERNMENT LICENSE RIGHTS STATEMENT

This invention was supported by funds from the U.S. Government (DARPAGrant No. N66001-97-1-8911 and DARPA Grant No. N66001-01-C-8056). TheU.S. Government may therefore have certain rights in the invention.

TECHNICAL FIELD

The invention relates to controlled, magnetohydrodynamically-driven,fluidic networks suitable for use in devices for processing andanalyzing biological and chemical samples such as laboratories on chipsand micro-total analysis systems. Placed within a temperature gradient,the fluidic networks of the present invention can further act as thermalcyclers, particularly of the type used for polymerase chain reactions(PCR). The invention also relates to magnetohydro-dynamic stirrers thatare capable of generating chaotic advection within a microfluidicconduit or chamber.

BACKGROUND

In recent years, there has been a growing interest in developing minutechemical and biological laboratories, analytical devices, and reactorsknown collectively as laboratories on chips. The ability to performchemical and biochemical reactions in such devices offers many benefitsincluding reduced reactant and media volumes for safety and economy, andimproved performance from increased thermal and mass transfer. In suchdevices, a spatially defined and controlled environment permits preciseflow of reactants through the network. The flow of a fluid from one partof the device to another, and the efficient mixing of fluids are tasksthat are far from trivial. In a micro-scale device such as a laboratoryon a chip, mixing of fluids is a particular challenge as flows are atvery low Reynolds numbers, turbulence is not available to promotemixing, and the insertion of moving components into these devices isdifficult.

Electrostatic forces have been used to move liquids around such devices.These forces usually induce only very low flow rates, require the use ofhigh electrical potentials, and can often cause significant heating ofthe solution which may be inappropriate for the materials being used orthe reactions to be performed. The use of electromagnetic forces offersa means for manipulating at least slightly conductive liquids inmicrofluidic devices and systems.

The application of electromagnetic forces to pump and/or confine fluidsis not new. It is known that magnetohydrodynamic (MHD) systems arecapable of converting electromagnetic energy into mechanical work influid media. To date, MHD systems have mostly been used to pump highlyconducting fluids such as liquid metals and ionized gases, to studyionospheric/astrophysical plasmas, and to control magnetic fusiondevices. Recently, however, MHD micro-pumps in silicon and in ceramicsubstrates have been constructed demonstrating the ability of such pumpsto move liquids through microscale conduits. These efforts, however,have addressed individual pumping devices and have not provided aneffective means for either the controlled movement of liquids through amicrofluidic network or the efficient mixing of liquids in suchmicroscale environments. Although it is envisioned that this inventionwill be mostly used in the context of minute devices, the concepts arenot limited for small devices and can be applied for large devices aswell.

Relevant publications, each of which are incorporated herein in theirentirety, are identified as follows:

-   Bau, H. H., 2001, A Case for Magnetohydrodynamics, Proceedings of    the 2001 ASME International Mechanical Engineering Congress and    Exhibition, New York, N.Y. 2001, November 11-16. CD. Vol 2.-   Bau, H. H., Zhong, J., and Yi, M., 2001, A Minute Magneto Hydro    Dynamic (MHD) Mixer, Sensors and Actuators B, 79/2-3, 205-213.-   Bau, H., H., Zhu, J., Qian, S., and Xiang, Y., 2003, A    Magneto-Hydrodynamically Controlled Fluidic Network, Sensors and    Actuators B, 88, 205-216-   Bau. H., H., Zhu, J., Qian, S., Xiang, Y., 2002, A    Magneto-Hydrodynamic Micro Fluidic Network, IMECE 2002-33559,    Proceedings of IMECE'02, 2002 ASME International Mechanical    Engineering Congress & Exposition, New Orleans, La., Nov. 17-22,    2002.-   Jang, V., and Lee, S. S., 2000, Theoretical and Experimental Study    of MHD (Magneto-hydrodynamic) Micropump, Sensors and Actuators A,    80, 84-89.-   Lemoff, A. V., and Lee, A. P., 2000, An AC Magnetohydrodynamic    Micropump, Sensors and Actuators B, 63, 178-185.-   Lee, A. P. and Lemoff, A., V., Micromachined Magnetohydrodynamic    Actuators and Sensors, U.S. Pat. No. 6,146,103.-   Qian, S., Zhu, J., and Bau, H. H., 2002, A Stirrer for    Magneto-Hydrodynamically Controlled Micro Fluidic Networks, Physics    of Fluids, 14 (10): 3584-3592.-   Yi, M., Qian, S., and Bau, H. H., A Magneto-hydrodynamic (MHD)    Chaotic Stirrer, J. Fluid Mechanics, 468, 153-177.-   Xiang, Y. and Bau, H. H., 2003, Complex Magneto Hydrodynamic, Low    Reynolds Number Flows, Physical Review Letters E, 68,    016312-1-016312-11.-   Zhong, J., Yi, M., and Bau, H. H., 2002, A Magneto Hydrodynamic Pump    Fabricated with Low Temperature Co-fired Ceramic Tapes, Sensors and    Actuators A: Physical, 96, 1, 59-66.

SUMMARY

One aspect of the present invention is a controlled,magnetohydrodynamically-driven, fluidic network comprising a pluralityof connected and individually controlled conduits each having at leastone pair of opposing walls and at least one pair of electrodes disposedalong the opposing walls, and at least one electrode controller inoperational engagement with the electrodes for implementing anactivation sequence comprising a current or potential across electrodepairs. In a preferred embodiment, the network further comprises analgorithm for determining the activation sequence. In operation, thefluidic network is provided with an at least slightly conductive fluid,is placed at least partially within a suitable magnetic field, and anelectric field of a specific current or potential is applied for apredetermined period of time across electrode pairs and through thefluid within the network. In accordance with MHD principles, themagnetic field is oriented approximately perpendicular both to theorientation of the electric field and to the axis of flow along theconduit. Interaction of the electric and magnetic fields generatevolumetric forces, called Lorentz body forces that propel the fluidthrough the network. By the selective application of electric fields ofspecific currents or potentials at various points in the network forspecific time intervals, the fluid may be directed with precisionthrough the network in any desired pattern without the need for movingparts such as mechanical pumps or valves. In this manner, the controland flow of fluid through the network is similar to the control and flowof an electrical current in an electronic circuit.

The fluidic network is controlled by means of at least one electrodecontroller in operational engagement with the electrodes positioned onthe sidewalls of the conduits. The controller or controllers implementan activation sequence of currents or potentials that are applied acrossthe electrode pairs of the network. In one embodiment, the activationsequence is determined in accordance with an algorithm. The algorithmcan be in any form that is capable of determining the magnitude,polarity and duration of current or potential across various electrodepairs throughout the network associated with generating a precisepattern of Lorentz forces for propelling the fluid in a controlledmanner along any desired path through the network including, forexample, an equation, a series of equations, a series of iterativesteps, or software. The activation sequence may be entirelypre-determined by the algorithm or determined with the use of feedbackgenerated by the operation of the network.

Another aspect of the invention is a controlled,magnetohydrodynamically-driven thermal cycler comprising the fluidicnetwork of the present invention positioned at least partially within atemperature gradient. The imposition of a temperature gradient acrossthe network allows fluid to move through one or more zones of differingtemperatures as it circulates within the network. By circulatingmaterials through different temperature zones, chemical and biochemicalreactions such as, for example, PCR may be readily accomplished. Thethermal cycler described herein may be used singly or in combination,and may operate either as part of an MHD-driven fluidic network, as acomponent in a non-MHD fluidic system, or as a stand-alone device.

Yet another aspect of the invention is a MHD stirrer for use inmicrofluidic networks. The MHD stirrer comprises a conduit or cavityhaving at least two electrodes disposed therein such that complexsecondary flows including flows characterized by chaotic advection aregenerated upon application of a current or potential across electrodepairs in a magnetic field. If two electrodes are used, at least oneelectrode must be movable between at least two positions to allow forthe alternating application of current or potential across theelectrodes in at least two different positions. If three or moreelectrodes are used, then the electrodes may be movable or fixedprovided that a current or potential is alternately applied betweenelectrode pairs in at least two different positions. In eitherembodiment, the application of a current or potential across theelectrodes induces at least two different alternating flow patternswhich in turn induces chaotic advection. The MHD stirrer may be usedsingly or in combination, and may operate either as part of anMHD-driven microfluidic network, as a component in a non-MHDmicrofluidic system, or as a stand-alone device.

A further aspect of the invention is a method for controlling the flowof fluid through a MHD-driven fluidic network comprising a plurality ofconnected and individually controlled conduits each having a pair ofopposing walls and at least one pair of electrodes disposed along theopposing walls, comprising the step of implementing an activationsequence of electrical currents or potentials across the electrode pairsby means of at least one electrode controller governed by an algorithmand in operable engagement with the electrode pairs.

Yet another aspect of the present invention is a method for generatingchaotic advection within a conduit or chamber of a microfluidic networkhaving at least two electrodes disposed therein comprising the step ofapplying an electrical current or potential across the electrodes togenerate at least two different alternating flow patterns and inducechaotic advection. In one embodiment, the current or potential isalternately applied between a stirring electrode and at least twodifferent electrodes disposed along the internal walls of the conduit.The two electrodes may be disposed on the same wall, on adjacent wallsor on opposing walls of the conduit. In an alternative embodiment, thecurrent or potential is alternately applied between one electrodedisposed along an internal wall of the conduit and at least two stirringelectrodes positioned within the conduit and away from the internalwall. In another embodiment, the polarity of the electric field betweenthe one or more stirring electrodes and the one or more electrodesdisposed along the internal walls is repeatedly reversed. The Lorentzforces generated by the configuration of electrodes and applied currentsor potentials within the conduit result in secondary flows, and inparticular flows characterized by chaotic advection, which are effectivein mixing laminar fluids such as fluids present within a microfluidicnetwork.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary and the following detailed description ofexemplary embodiments of the invention are better understood when readin conjunction with the accompanying drawings.

FIG. 1 a is a top view of a conduit of a MHD microfluidic network;

FIG. 1 b is a cross-section view of the conduit shown in FIG. 1 a;

FIG. 2 a is a cross-section view of an arrangement of electrodes withina conduit in accordance with one embodiment of the invention;

FIG. 2 b is a cross-section view of an arrangement of electrodes withina conduit in accordance with another embodiment of the invention;

FIG. 3 a is a top view of a microfluidic network lacking physical wallswith its conduit boundaries defined by the layout of electrodes;

FIG. 3 b is a cross-section view of the microfluidic network shown inFIG. 3 a;

FIG. 4 is a schematic representation of a fluidic network withindividually-controlled branches numbered 1 through 6 and nodes labeleda through e. An inlet port is located at node a, and exit ports arelocated at nodes c and e;

FIG. 5 is a schematic representation of a MHD fluidic network withindividually-controlled branches numbered 1 through 9 and reagentreservoirs denoted R₁ and R₂;

FIG. 6 is an exploded view of the fluidic network shown schematically inFIG. 5 depicting the layers used in the construction of the device;

FIG. 7 is a schematic representation of a MHD network that can be usedfor combinatorial interactions;

FIG. 8 depicts a time-series of images of the predicted and observedstirring of a drop of material inserted in the conduit when two internalelectrodes are alternately engaged;

FIG. 9 is a cross-section view of a cylindrical MHD stirrer having twointernal, eccentrically-located electrodes A and B and a peripheralelectrode C;

FIGS. 10 a through 10 i depict Poincar sections (stroboscopic images) ofthe trajectories of passive tracers (FIGS. 10 a through 10 c), actualpassive tracers' trajectories (FIGS. 10 d through 10 f), and flowvisualizations (FIGS. 10 g through 10 i) of traces of a drop of dyeinserted in the cavity as functions of the alternations period (T);

FIG. 11 is a schematic representation of another embodiment of a MHDstirrer in which the electrodes are transverse to the conduit's wallsand they are labeled Ai (i= . . . −2, −1, 0, 1, 2, . . . );

FIG. 12 depicts flow visualization experiments using a stirrerconfigured as depicted in FIG. 11;

FIG. 13 illustrates the device depicted in FIG. 11 inducing chaoticadvection by the deformation of a straight line of dye initiallyinjected midway between the conduit's walls through the application ofalternating potential differences between the evenly and oddly numberedelectrodes. The figures in the left and right columns correspond,respectively, to theoretical predictions and experimental observations;and

FIG. 14 depicts schematically a continuous flow thermal cycler that canbe used for PCR. A1, A2, B1, B2, C1, C2, D1, and D2 are electrodes. Thedifferent shades of gray scale denote zones maintained at differenttemperatures.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Controlled-flow MHD fluidic networks, thermal cyclers, and chaoticadvection stirrers for use in microfluidic devices for processing andanalyzing biological and chemical samples such as laboratories on chipsand micro-total analysis systems are described.

The controlled-flow MHD fluidic network comprises a plurality ofconnected and individually controlled conduits for the transmission offluid each conduit having a pair of opposing walls, at least one pair ofelectrodes disposed along the opposing walls of the conduits, and atleast one electrode controller in operational engagement with theelectrodes for implementing an activation sequence of currents orpotentials across the electrode pairs. In preferred form, the networkfurther comprises an algorithm for determining the activation sequence.Movement of fluid through the network is accomplished in accordance withprinciples of magnetohydrodynamics which utilize the interaction ofapproximately perpendicularly oriented electric and magnetic fields togenerate Lorentz forces within the network. The pattern of Lorenz forcesmoving fluid through the network is governed by the activation sequencewhich defines the particular magnitude, polarity and timing of currentor potential to be applied across individual electrode pairs. Theactivation sequence itself is determined by an algorithm which mayproduce a predetermined activation sequence or a sequence which usesinformation about the state of the fluidic network or of the fluidcirculating within the network during operation of the network. In thismanner, fluid within the network that is at least slightly conductivemay be directed with precision and control through the network along anydesired path and without the need for mechanical valves or pumps.

The basic building block of the controlled-flow MHD fluidic network isthe conduit. Described generally with reference to FIGS. 1 a and 1 b,the individual conduit of the fluidic network has length L, width W, andheight h. The conduit may be capped, as depicted in FIGS. 1 a, 1 b, 2 aand 2 b, or open from above as shown in FIG. 6. Moreover, conduitscomprising a network of conduits may have the same or different shapes,lengths and sizes provided that the conduits are capable of bearingelectrodes positioned suitably for the generation of Lorentz forces uponthe application of a current or potential within a magnetic field.Suitable configurations include, for example, rectangular, as shown inFIGS. 2 a and 2 b. Alternatively, the conduits may comprise straight,curved or slanted walls that in cross-section are square, trapezoidal,circular, oval, or any other such suitable shape or combination ofshapes.

The network of conduits may be simple or complex comprising anycombination of curved or straight conduits with few or manyinterconnections arrayed in either two or three dimensions. A networkcomprising solely of straight conduits is shown in FIG. 7, and FIG. 5depicts an example of a network comprising a combination of straight andcurved conduits. Further, FIGS. 4, 5, and 7 provide schematic depictionsof embodiments of relatively simple, two-dimensional networks. In FIGS.4 and 5, the individual conduits, similar in structure to the conduitdepicted in FIGS. 1 a and 1 b, are denoted with numbers. The network canbe connected to external supplies and drains denoted as a, c, and e inFIG. 4. Alternatively, fluid can circulate inside the network withoutexternal links as shown in FIG. 5.

The MHD-controlled networks can be fabricated from a variety ofsubstrate materials including, for example, silicon, monomers,prepolymers, polymers, elastomers, glass, plastics, metals (incombination with dielectric materials) and ceramic materials such as,for example, low temperature, co-fired ceramic tapes. Ceramic tapes area convenient substrate material as they are dielectric and amenable tolayered manufacturing techniques. Individual tapes may be machined andelectrodes, conductors, and resistors may be printed or otherwiseapplied on the tapes with metallic pastes or inks in their green(pre-fired) state when the tapes are soft and pliable. A plurality ofindividually processed tapes can then be stacked, aligned, laminated,and co-fired to form a monolithic device that integrates hydraulicconduits and conductive paths arrayed in a two or three dimensions. Suchmanufacturing techniques also provide a means for inexpensive and rapidprototyping. Ceramic tapes may further include magnetic materials suchas magnetic particles thus integrating the magnetic field source intothe substrate and eliminating the need for the use of external magnetsto generate Lorentz forces within the network.

In the pre-fired (green) state, ceramic tapes may comprise oxideparticles such as alumina and/or silica, glass frit, and an organicbinder that can be made from photo-resist. The tapes are available in avariety of thicknesses, typically from about 100 flm±7% to a few hustredmicrons, although thinner tapes of about 40 flm can be casted. The tapesin their green state are soft and pliable, and can be readily machinedby a variety of known techniques including laser, milling, andphotolithography when the binder is photo-resist. Conductive paths suchas metallic circuits may be either printed, processedphotolithographically, or otherwise applied to the tapes to formelectrical circuits and components such as electrodes, resistors,conductors, and thermistors. Conduit sizes may be any size suitable foruse in MHD-driven fluidic networks, and in one embodiment may range fromabout 10 flm to several millimeters. Individual tapes may be stacked,aligned, laminated, and co-fired to form sintered, monolithic structureshaving complex, either two- or three-dimensional networks of fluidicconduits, electronic circuits, and electrodes. Glass or other materialscan be attached to or incorporated in the tapes to facilitate opticalpaths. Further, the tapes may include a magnetic material such asmagnetic particles and/or a single or multiple layers of coils may beembedded in the tapes to generate a magnetic field.

The conduits of the fluidic network are provided with at least one pairof electrodes (denoted in FIGS. 1 a and 1 b as C_(u) and C_(n) of lengthL_(e)) positioned on opposing internal surfaces of the conduit. Theseelectrodes, referred to as driving electrodes, define the region alongthe conduit in which an electric current or potential is applied. Thedriving electrodes may be positioned on the internal surfaces of theconduits in a variety of ways all of which are considered within thescope of the invention. Two such electrode configurations are depictedin FIGS. 2 a and 2 b. FIG. 2 a depicts an arrangement of electrodescomprising four individual electrodes positioned along the corners of aconduit as shown in cross-section. FIG. 2 b depicts an arrangement ofelectrodes comprising a pair of individual electrodes each covering theentire area of opposing sidewalls of a conduit. The arrangement ofelectrodes as shown in FIG. 2 b is a configuration that can provide anearly uniform current density in a fluid within the conduit. Electrodesmay also be used to control the shape of the velocity profile and,depending on the specific application, arrangements other than thoseshown in FIGS. 2 a and 2 b may be preferable.

It is further aspect of the invention that not every individual conduitwithin the network need be provided with driving electrodes providedthat conduits that are not so equipped are in communication with atleast one conduit that is so equipped. In this manner, the propulsion offluid through the conduit having driving electrodes is capable ofdriving fluid through the conduit lacking such electrodes. In preferredform, the driving electrodes terminate some distance away from the endsof the conduit so as to minimize current leakage (cross-talk) between oramong adjacent conduits comprising the network.

The driving electrodes themselves may be used to form virtual conduits,that is, conduits which lack physical walls for the containment of thefluid. Flow of fluid through a network comprising virtual conduits isspatially defined by the configuration of the electrodes on thesubstrate and controlled by the current or voltage applied acrosselectrode pairs. In such networks, the electrodes may either protrudefrom, be flush with, and/or terminate beneath the surface of thesubstrate. FIGS. 3 a and 3 b depict an example of a toroidal virtualconduit and a straight virtual conduit in which the “walls” of theconduits are the electrodes themselves. FIGS. 3 a and 3 b correspond,respectively, to a top view and a view in cross-section of the virtualconduits. Complicated patterns of electrodes may be readily manufacturedusing a variety of printing and lithographic techniques for applying theelectrodes to the substrate.

Each pair of driving electrodes is in operable engagement with anelectrode controller that acts to control the magnitude, polarity andtiming of the current or potential applied across pairs of drivingelectrodes. The network may comprise a single electrode controller inoperable engagement with each of the driving electrodes of the network.Alternatively, the network may comprise a plurality of electrodecontrollers each of which controls one or more driving electrodes of thenetwork. In one embodiment, each pair of driving electrodes iscontrolled by a separate electrode controller. By controlling thecurrent and/or potential applied across each electrode pair, the one ormore electrode controllers regulate in a precise pattern and withprecise timing the generation of Lorentz forces that propel the fluidthrough the conduits of the network. An implementation of an exemplaryelectrode controller and algorithm are described in greater detail inBau, H., H., Zhu, J., Qian, S., and Xiang, 2003, Y., AMagneto-Hydrodynamically Controlled Fluidic Network, Sensors andActuators B: Chemical, 88, 205-216, which is incorporated herein in itsentirety.

The one or more electrode controllers of the network are governed by anactivation sequence that coordinates and controls the flow andcombination of fluids within the network. In one embodiment, theactivation sequence is determined in accordance with an algorithm whichcomputes and defines the magnitudes, polarities and timing of currentsor potential differences applied across the various driving electrodepairs of the network that are necessary to achieve the desired controlof flow paths and flow rates throughout the network. The algorithm canbe in any form that is capable of determining the specific current orpotential across various electrode pairs throughout the networkassociated with generating a precise pattern of Lorentz forces forpropelling the fluid in a controlled manner along any desired paththrough the network including, for example, an equation, a series ofequations, a series of iterative steps, or software. In one embodiment,the user specifies the desired flow path and the flow rates associatedwith the various conduits. The algorithm then computes the magnitudes,polarities and timing of currents or the voltages that are needed toimplement the desired conditions. The algorithm may also compute themagnitudes, polarities and timing of currents or voltages whileminimizing an objective function such as, for example, the total powerdissipation of the device. The sequence of specific magnitudes,polarities and timing of currents or voltages across particularelectrode pairs comprises the activation sequence that is used by theelectrode controllers to generate the Lorentz forces necessary to propelfluid in the network along the desired flow path.

Preferably, the algorithm is in the form of a software program capableof calculating specific magnetic and/or electric field strengthsassociated with flow rates within conduits of a known size. As asoftware program, the algorithm may be resident on the one or moreelectrode controllers or located remote from the controllers providedthe activation sequence generated by the algorithm is capable ofcommunication with and implementation by the one or more electrodecontrollers. The algorithm may determine the magnitude, polarity andtiming of current or potential in a predetermined mode or in a mode thatuses feedback generated by the operation of the network in determiningthe activation sequence. In embodiments in which the activation sequenceis determined at least partially with the use of feedback, the networkfurther comprises a sensor assembly capable of continuously orperiodically collecting information about the state of the network orthe fluid circulating within it during operation and inputting thisinformation into the algorithm. MHD-driven fluidic networks in whichmovement through the network can be controlled by an activation sequencegenerated by an algorithm are suitable for a variety of applicationsincluding point-of-care medical diagnosis; laboratory diagnosis; drugdiscovery; air, food, and water quality monitoring; and detection ofpathogens and chemical agents associated with biological and chemicalwarfare agents.

In accordance with MHD principles, the orientation of the magnetic fieldneed not be vertical with respect to a conduit oriented in a horizontalplane. For example, if a pair of driving electrodes were positioned onthe top and bottom walls of the conduit oriented in a horizontal plane,MHD principles would require the magnetic field to be oriented alsohorizontally but transverse to the direction of flow of the conduit.Thus, the controlled-flow MHD fluidic network of the present inventionmay accommodate any combination of electrical and magnetic fields thatare approximately perpendicular to each other and in any orientationwith respect to the conduit provided both fields are approximatelyperpendicular with respect to the axis of flow through the conduit. Inone embodiment, the conduits comprising the network are arranged in aplanar configuration and the magnetic field is oriented approximatelyperpendicular to the plane in which the conduits are arrayed.

As shown in FIGS. 1 a and 1 b, a three-dimensional Cartesian coordinatesystem can be represented with respect to an exemplary conduit of thenetwork by axes x₁, x₂, and x₃. The vertical arrow denoted with theletter (B) indicates the orientation of the magnetic field. Inoperation, the entire device is subjected to a magnetic field of aspecific intensity. The magnetic field may be generated by a permanentmagnet or an electromagnet. Alternatively, the entire network may befabricated with the inclusion of a magnetic material, therebyeliminating the need for an external magnetic field source. The mostsuitable source for the magnetic field will depend on a variety offactors including the particular application for which the network isintended. In other embodiments, synchronized, alternating electric andmagnetic fields may also be used. In such embodiments, the fields may besynchronized such that the resulting Lorentz forces remains essentiallysteady.

Fluid is transmitted from one region of the MHD network to another bycurrents I_(i) or potential differences V_(i) applied across the drivingelectrode pairs within the conduits of the network. The potentialdifference V_(i) in a given conduit (i) induces an electric current ofdensity J_(i-s) _(i) V/W_(i) where W_(i) is the conduit's width ands_(i) is the specific electric conductivity of the fluid. This current,in turn, interacts with the magnetic field to produce a Lorentz bodyforce of density (J_(i)B) directed along the axis of the conduit. Themagnitude of the force and its direction may readily be controlled byrespectively controlling the magnitude and polarity of either thepotential difference V_(i) or the current I_(i). Since the relationshipbetween the flow rate and the current is linear over the domain ofinterest, the electric current typically will be the preferred controlvariable. To a first approximation, the flow rate (Q_(i)) in the conduitis given as a function of the potential difference V_(i) (or the currentI_(i)), and the pressure drop across the length of the branch (DP_(i))by the constitutive relationships of the type: Q_(i)=H_(i)DP_(i)+M_(i)^(v)Vi or Q_(i)=H_(i)DP_(i)+M_(i) ^(I)I_(i) where H_(i) and M_(i) are,respectively, the hydraulic and MHD conductivities. Preferably, theconduits comprising the network are sufficiently long so that fringeeffects can be neglected, and the current flow is essentiallyone-dimensional.

An exemplary MHD-controlled fluidic network is shown in FIG. 4. Theindividual conduits comprising the network are denoted by the numbers 1through 6 and the nodes are denoted with the letters a through e. Nodesa, c, and e communicate beyond the network or with reagent reservoirsand serve as sinks and sources. In an alternative embodiment, thenetwork is not provided with any sinks or sources. Conduits which do notcontain driving electrodes have hydro-magnetic conductivity set to zero.For the network depicted in FIG. 4, six equations relate the flow ratein a conduit to the pressure drop along that conduit's length and thepotential difference across the electrodes. Additionally, masscontinuity (Kirchhoffs law) requires that all the flow rates arriving ateach node sum up to zero. When the potential differences across all theconduits and the pressures at the sources and sinks are given, theseequations can be solved to obtain the flow rates in all the conduits.

An embodiment of the network as shown in FIG. 5 is manufactured with lowtemperature, co-fired ceramic tapes. The device has planar architecture,that is, all the conduits of the network are arrayed in a single layer.While the single conduit layer shown in FIG. 5 consists of a pluralityof tapes, an individual layer may be formed from a single tape or from aseries of tapes depending on the thickness of the tapes and the desiredlayer thickness. In an alternative embodiment, conduits may befabricated in multiple layers and interconnected through one or morevertical wells to form a network comprising a three-dimensional array ofconduits.

In one embodiment, a planar, MHD-controlled fluidic network isfabricated with LTCC 951AX co-fired ceramic tapes supplied by DuPontthat have a nominal (pre-fired) thickness of ˜250 μm. FIG. 6 provides anexploded view of the elements of the network as shown schematically inFIG. 5. The fabrication process consists of blanking rectangularsegments of tapes to a desired size. A few layers of tapes are laminatedto form a part. The various parts are machined individually using anumerically-controlled milling machine. Subsequently, electrodes andconductor paths are printed on the various parts.

In one embodiment as shown in FIG. 6, layer A is the top layer thatcontains the flow conduits and includes 1.1 mm wide×1.7 mm deep flowconduits and soldering pads using DuPont 6134 solderable conductors. Thesoldering pads are connected through vertical vias filled with DuPont6141 via fill paste to the various electrodes. While relatively largeconduits are fabricated in this embodiment to facilitate easy flowvisualization, similar networks may be fabricated having much smallerdimensions. Layer B comprises the bottom wall of the conduits andcontains the electrodes and some of the electrical leads connecting tothe electrodes. A more detailed layout of the electrodes shown in layerB is provided in insert E. About 20 μm thick×2 mm wide electrodes madefrom DuPont 5734 gold paste are printed on the surface of layer B. Thegold electrodes are aligned with the edges of the conduits such thatwhen layers A and B are attached, about 0.1 mm of the widths of theelectrodes along each side of the conduits' vertical walls are exposedto the conduits. Each conduit is provided with a pair of drivingelectrodes. A gap separates the driving electrodes in adjacent conduits.Silver conductors made from DuPont 6145 conductor paste are printed onboth layers B and C to facilitate the connection of each electrode tothe soldering pads located on the surface of layer A. All the leads areconnected through vertical vias to terminals located on the surface oflayer A. Layer D, the bottom layer, contains additional leads.Subsequent to machining and printing, the individual parts are stacked,aligned, laminated, and co-fired to form a sintered, monolithic block.The device may capped with a cover plate or left uncapped to facilitateeasy access to the channels and to enable dye injection for flowvisualization.

In one embodiment, the electrodes of the network may be controlled by anelectrode controller comprising computer-controlled relay actuators andaD/Icard. The relays are programmed to switch on and off in such a waythat any one or combination of electrode pairs in the network can beactive at any given time and for any given interval. Additionally, therelays allow for the switching of the polarity of any given pair ofelectrodes and the supply of power either in controlled-voltage orcontrolled-current modes.

In operation, the conduits are filled with a fluid that is at leastslightly conductive such as, for example, saline solution. While 0.1Mand 0.3M solutions are suitable, MHD-driven networks can operate withion concentrations as low as about 50 mM. The device is placed on top ofa neodymium (NdFeB) permanent magnet of approximate intensity B=0.4T(Edmund Scientific). Dye (Cole Parmer Instrument Co.) is injected atvarious locations to achieve flow visualization.

The fluidic network may be analyzed using linear graph theorymethodology, and the potentials Vi or currents Ii may be determined soas to direct the fluid to follow any desired path. In one set ofexperiments utilizing a network configured as shown in FIG. 5, a traceof dye was inserted into the fluid at conduit 1. The electrodes of allthe conduits were activated, and the network was programmed to pump thefluid around the large circuit (conduits 1, 2/3, 4, 5/6 and 7) with theflow divided between conduits 2 and 3 and between conduits 5 and 6. Byappropriate choice of current or potential differences, the flow can besplit between conduits 2 and 3, and between conduits 5 and 6 in anydesired proportion. When the dye entered the torus comprising conduits 2and 3, the electrodes within all the conduits but 2 and 3 were switchedoff. The polarity of conduit 3's electrodes was reversed, and the fluidwas forced to circulate around the torus. In one embodiment, the toruscan be positioned across a temperature gradient having two or moredifferent temperature zones such as may be needed for DNA amplificationreactions. Subsequently, the polarity of electrodes in conduit 3 wasreset to its original setting, all the other electrodes were turned on,and the dye was pumped out of the torus into conduit 4. The dye thensplit between conduits 5 and 6 and recombined in conduit 7. Byappropriate choice of current or potential differences, the flow can bemade to circulate around the loop consisting of conduits 6 and 7. In analternative network, liquids are pumped from the wells at the end ofconduits 8 and 9, the fluids are mixed in conduit 1 equipped withstirring electrodes as described herein, and the electrodes areprogrammed to pump the liquid into the torus defined by conduits 2 and3.

FIG. 7 depicts schematically a more complicated MHD network consistingof a plurality of wells R and conduits 10 through which reagents,analytes, or chemicals may be pumped along any desired path and stirred,causing various interactions and/or reactions. Each of the conduitsshown in FIG. 7 has a structure similar to the conduit depicted inFIG. 1. Analytes and reagents may be pumped from any of the wells,brought together, and mixed to interact and/or react with reagentspumped from other wells. The network may also facilitate combinatorialscreening in which many processes are carried out in parallel. Moreover,reaction and interaction products may be used in subsequent reactions orinteractions in either predetermined or feedback modes. The embodimentdepicted in FIG. 7 can readily be expanded to a three-dimensionalnetwork allowing a much larger number of connections. These examplesillustrate that MHD-controlled networks provide an easy, effective andinexpensive way of circulating fluids through microfluidic laboratory ona chip conduits.

MHD-controlled networks can operate with a wide variety of electrolyteand buffer solutions such as, for example, solutions containing NaCl,KCl, NH₄Cl, CuSO₄, FeCl₂/FeCl₃, NaH₂PO₂, and Hydroquinone among manyothers. The performance of the device, however, may be affected by theparticular solution and electrode materials that are used. For example,the use of NaCl solutions may lead to bubble production at relativelyhigh current densities and electrode corrosion. To the extent MHD-drivendevices are used as disposable devices, electrode corrosion may not bean issue of significance. Moreover, the MHD-driven devices, depending onthe application, can operate either open or capped. With open conduits,bubble formation may not present a problem. In closed conduits, however,bubble generation must be addressed and preferably limited. In oneembodiment, the use of redox species such as FeCl₂/FeCl₃ solution withplatinum electrodes may sustain higher current densities than a NaClsolution without bubble formation and without electrode corrosion.Ultimately, though, the choice of the electrolyte or buffer is dictatedby, among other things, the compatibility of the electrolyte or bufferwith the specific processes to be performed in the system. In additionto the MHD forces, the fluid within the network may also be subject to apressure gradient that is either flow assisting or flow adverse.

Another aspect of the present invention is an MHD stirrer. Chemicalreactions and biological interactions in a microfluidic device ofteninvolve mixing or stirring fluids in order to bring various moleculestogether. Mixing by diffusion alone in a microfluidic device is oftennot efficient. The diffusion time of macromolecules may be prohibitivelylarge even when the lengths are measured in hundreds of microns.Moreover, since flows are often laminar and corresponding Reynoldsnumbers in microdevices are usually very small, one is also denied thebenefits of turbulence as an efficient mixer.

In one embodiment, the MHD stirrer of the present invention comprises aconduit or chamber having at least two electrodes disposed therein suchthat the application of a current or potential across the electrodeswithin a magnetic field generates secondary flows such as flowscharacterized by chaotic advection. In embodiments in which twoelectrodes are used to induce chaotic advection, at least one electrodemust be movable so that the current or potential may be appliedalternately across electrode pairs in at least two positions. Inembodiments in which at least three electrodes are used, the electrodesmay be movable or fixed and disposed along and/or away from the internalwalls of the conduit or chamber. In either embodiment, a current orpotential is alternately applied across electrodes occupying at leastthree positions to induce at least two alternating flow patterns whichgenerates chaotic advection.

In one embodiment, the MHD stirrer of the present invention comprises aconduit having at least one electrode disposed along the wall of theconduit, and at least two electrodes positioned within the conduit andaway from the wall. In another embodiment, the MHD stirrer comprises atleast two electrodes disposed along at least one wall, and at least oneelectrode positioned within the conduit and away from the wall. In afurther embodiment, the stirrer has at least two electrodes alignedalong at least one wall, and at least one electrode disposed alonganother wall. In yet another embodiment as shown in FIGS. 1 a and 1 b,the MHD stirrer comprises a pair of electrodes disposed along theopposing walls, and at least two electrodes positioned within theconduit and away from the opposing walls. In this embodiment, theelectrodes positioned within the conduit and away from the opposingwalls may be aligned as shown in FIG. 1 a along the centerline of theconduit's bottom. In still another embodiment, the MHD stirrer comprisesa cylindrical chamber with an electrode disposed around its internalperiphery and at least two electrodes positioned eccentrically insidethe chamber. The placement of the one or more electrodes permits thegeneration of complex secondary flows including flows characterized bychaotic advection that is beneficial for mixing or stirring within afluidic conduit or chamber. The conduits as described in all of theseembodiments may comprise a conduit of the MHD-driven fluidic network orthermal cycler of the present invention.

MHD stirrers that generate chaotic advection may operate either byvarying the current or potential applied across electrode pairs betweenzero and a prescribed value (either positive or negative) or byrepeatedly reversing the polarity of each electrode by varying thecurrent or potential between negative and positive values. Depending onthe particular electrolyte used, reversal of polarity may beadvantageous in certain cases since by reducing electrode corrosion andbubble accumulation on electrode surfaces. Furthermore, in applicationsin which analyte migration in the electric field is a problem, reversingpolarity is likely to reduce or eliminate such migration.

In the embodiment shown in FIGS. 1 a and 1 b, a conduit of a controlled,MHD-driven microfluidic network is provided with a pair of electrodesdisposed on opposing walls of the conduit and a series of electrodesdenoted Ai disposed along the centerline of the conduit and away fromthe opposing walls. Electrodes Ai (where i=1, 2, 3, . . . ) are referredto as stirring electrodes. This particular implementation of the stirreris described in greater detail in Qian, S., Zhu, J., and Bau, H. H.,2002, A Stirrer for Magneto-Hydrodynamically Controlled MicroFluidicNetworks, Physics of Fluids, 14 (10): 3584-3592 which is incorporatedherein in its entirety.

In order to operate a MHD conduit as a stirrer, the electrodes intendedfor use in creating secondary flows are in operable engagement with atleast one electrode controller such as, for example, acomputer-controlled relay actuator. In one embodiment, relay-actuatorscombine both driving electrodes and into a single electrode C. When apotential difference is applied across the electrode pair C-A_(i),circulatory motion of the fluid within the conduit is generated, withthe fluid circulating around electrode A_(i). When the electrode pairC-A₁ is pair C-A₁ once again, and so on in a periodic fashion, chaoticadvection is generated. As the magnitude of the period (T=T₁+T₂)increases, the chaotic region increases in size and complexity. In somecircumstances, it may be advantageous to alternate the electrodepotentials in a non-periodic fashion.activated for a time interval T₁,electrode pair C-A₂ for another time interval T₂, then electrodepotentials in a non-periodic fashion.

In demonstrating this effect, flow visualization experiments of thestretching and deformations of a dye blob were performed. FIG. 8 depictscomputational and experimental results when a blob of dye was insertedinto the conduit and the evolution of the dye was tracked over time.Both in experiment and theory, a rapid spread of the dye was observedindicating efficient stirring. By engaging a larger number of electrodepairs C-A_(i), one can further extend the fraction of the conduit thatparticipates in the mixing process. As electrodes may be readilypatterned into various shapes, electric fields may be induced indifferent directions. The interaction of such electric fields with themagnetic field can be used to induce secondary complex flows that may bebeneficial for stirring and mixing.

Stirring electrodes such as electrodes Ai shown in the embodimentdepicted in FIGS. 1 a and 1 b may be located singly or in combinationanywhere within a conduit provided they are away from either of theopposing walls. The electrodes need not to be aligned along theconduit's center. Although it is convenient to print the electrodes onthe device's floor to avoid intrusion, one can also use otherarrangements such as, for example, electrodes in the form of pins thatprotrude into the conduit.

The MHD stirrer may comprise either an open or a closed cavity of anysuitable shape. With reference to FIG. 9, an embodiment of the stirreris described comprising a circular cavity with an electrode C depositedalong its periphery. Two additional electrodes, A and B, are depositedon the cavity's bottom. The cavity is filled with a conducting liquidsuch as, for example, a saline solution, and it is positioned in auniform magnetic field oriented parallel to the cavity's axis. When apotential difference is imposed across the two electrodes A and C, anelectric current flows between the two electrodes and the interactionbetween this current and the magnetic field results in Lorentz forcesthat induce, for example, counterclockwise flow circulation in thecavity centered next to the location of electrode A. Subsequently, whenthe potential difference is switched from electrode pair A/C toelectrode pair B/C, depending on the polarity of the electrodes, eithera counterclockwise or a clockwise circulatory pattern may be inducedcentered next to the location of electrode B. The device is operated byalternately engaging electrode pairs A/C and B/C with a period T. Insome circumstances, it may be advantageous to alternate the electrodepotentials in a non-periodic fashion.

FIGS. 10 a through 10 i depict Poincare sections (stroboscopic images)of the trajectories of passive tracers (FIGS. 10 a through 10 c), actualpassive tracers' trajectories (FIGS. 10 d through 10 f), and flowvisualizations (FIGS. 10 g through 10 i) of traces of a drop of dyeinserted in the cavity as functions of the normalized (dimensionless)alternations period (T). The columns of FIGS. 10 a, 10 d and 10 g), (10b, 10 e and 10 h) and (10 c, 10 f and 10 i) correspond, respectively, toT=2, 6 and 8. When T=2, the motion depicted in the Poincare sectionshown in 10 a is mostly regular and consists of two sets of closedorbits, one set encircling one electrode and the other set encirclingthe other electrode. FIG. 10 d depicts the actual motion of the tracerwhich shows the presence of jitters resulting from the tracer beingtrapped (at different times) by the flow fields induced by the twoelectrode pairs. The presence of two families of periodic orbits is wellsupported by the flow visualization experiments as shown in FIG. 10 g.

As the period T increases, chaotic islands become visible. FIG. 10 eillustrates that as the period increases, so does the magnitude of thejitters. The presence of the global structure consisting of twocounter-rotating circulations is visible in FIG. 10 h. When T=8, FIG. 10c depicts the trajectory of a single tracer. The irregular chaoticregion appears to have spread to cover almost the entire cavity. Similarto FIG. 10 c, the flow visualization experiments depicted in FIG. 10 iillustrate the presence of counter-rotating eddies through the existenceof an unmixed zone at the ends of the diagonal that is perpendicular tothe line connecting the two electrodes. The operation of the device isdescribed in greater detail in Yi, M., Qian, S., and Bau, H. H., AMagneto-hydrodynamic (MHD) Chaotic Stirrer, J. Fluid Mechanics, 468,153-177 (2002) which is incorporated herein in its entirety.

FIG. 11 depicts a schematic representation of another embodiment of aMHD stirrer. As shown in FIG. 11, the stirring electrodes are alignedperpendicular to the conduit's walls. By subjecting these electrodes tovarying potential differences in the presence of a magnetic field,forces are generated that drive fluid flow in various directions in“virtual” conduits whose geometry is dictated by the positioning of theelectrodes. An implementation of the stirrer is described in greaterdetail in Bau, H. H., Zhong, J., and Yi, M., 2001, A Minute MagnetoHydro Dynamic (MHD) Mixer, Sensors and Actuators B, 79/2-3, 205-213; andXiang, Y. and Bau, H. H., 2003, Complex Magneto Hydrodynamic, LowReynolds Number Flows, Physical Review Letters E, 68,016312-1-016312-11, which are incorporated herein in their entirety.

FIG. 12 depicts the deformation of an initially straight dye lineresulting from the application of Lorentz forces by means of a MHDstirrer of the present invention. A thin trace of dye (Water SolubleFluorescent Liquid Dye, Model298-16-Red, Cole Palmer Instrument Company,Niles, Illinois, USA) is applied by means of a syringe across the cavityand then a potential difference is applied across adjacent electrodes.As a result of the application of the potential difference, fluid flowis induced in the cavity. The motion consists of rotating cells with thefluid moving up in one interval between two electrodes and down in theadjacent interval. Frame A in FIG. 12 depicts the line of dye initiallyinserted into the device. Depending on the polarity of the electrodes,the dye either moves upwards or downwards as shown in frame B of FIG.12. After a few seconds, the polarity of the electrodes is reversed.Since diffusion is relatively slow and the flow is at a relatively lowReynolds number, the dye retracts its steps in almost a reverse fashionas shown in frame C of FIG. 12 and then starts deforming in the oppositedirection as shown in frame D of FIG. 12. When the process is allowed tocontinue for some time, the dye traces the convective cells as shown inframe E of FIG. 12 in good qualitative agreement with theoreticalpredictions.

The electrodes may be patterned in many different ways to induce variousflow patterns. The embodiments described above are just a few examplesof numerous possible variants of MHD stirrers.

FIG. 13 compares theoretical predictions shown in the left column andexperimental results shown in the right column obtained in anotherimplementation. FIG. 13 depicts the deformation of an initially straightline of dye under various operating conditions. The top row depicts theflow structure when only the odd-numbered electrodes are active. Byalternating the potential difference across non-adjacent pairs ofelectrodes, it is possible to induce chaotic motion in the cavity. Forexample, electrodes A⁻², A₀, and A₂ may be engaged for the time intervalT₁, and then electrodes A⁻¹ and A₁ for the time interval T₂. Byrepeating this mode of operation, fairly complicated flows are generatedand effective stirring is provided. The results of this mode ofoperation are depicted in the bottom row of FIG. 13.

Another aspect of the invention is a controlled, MHD-driven thermalcycler comprising the fluidic network of the present inventionpositioned at least partially within a temperature gradient.Magnetohydrodynamics provides the means to circulate fluids continuouslyin a closed loop. Different parts of the loop may be maintained atdifferent temperatures, enabling the cycling of the liquid to subjectthe liquid to different temperature zones.

FIG. 14 depicts one embodiment of the thermal cycler of the presentinvention. The cycler comprises a closed conduit loop with electrodesaligned along opposing walls. Electrodes A1 and B1 are aligned along theinner wall of the loop, and electrodes A2 and B2 are aligned along theouter wall of the loop. An entry port with electrodes C1 and C2 alignedalong its opposing walls leads into the loop and an exit port withelectrodes D1 and D2 aligned along its opposing walls leads out of theloop. While the device shown in FIG. 14 has one inlet and a separateexit port, the cycler may be equipped with a single port or largernumber of inlet and exit ports. In order to utilize the conduit loopdepicted in FIG. 14 as a thermal cycler, different parts of the loop aremaintained at different temperatures. The various temperature zones maybe maintained, for example, with the use of electrical resistors orthermoelectric units (not shown). FIG. 14 depicts three thermal zones.It is contemplated as within the scope of the invention that a larger ora fewer number of thermal zones may be used as is suitable withreference to the particular application.

At the beginning of operation, an electrical potential is applied to theelectrodes such that the material is drawn into the loop. The polaritiesof either electrode pair A1 and A2 or electrode pair B1 and B2 are thenreversed so that the material within the conduit loop is forced tocirculate continuously around the loop. The particular choice ofpolarity will determine whether the motion is in the counterclockwise orclockwise direction. If necessary, the polarities and the magnitudes ofthe potentials applied to electrodes C1, C2, D1, and D2 may be adjustedso as to prevent the material within the conduit from leaving the loop.Also, if necessary, the direction of the flow in the thermal cycler maybe periodically changed to minimize analyte migration in the electricfield. As the material within the conduit cycles around the loop, it isexposed to different temperatures. In certain embodiments, this cyclingbetween or among different temperature zones facilitates biologicalinteractions such as, for example, those needed for PCR.

After the material within the conduit has completed the desired numberof cycles around the loop, electrical potentials are supplied to thevarious electrodes so as to pump the reaction products out of the loop.The reaction products may be pumped either through the exit port definedby electrodes D1 and D2, back through the inlet port defined byelectrodes C1 and C2, or split among any number of exit ports (not shownin the figure) so as to transport parts of the sample to differentsubsequent analysis paths. The embodiment of the MHD thermal cyclerdepicted in FIG. 14 may be readily integrated into amagneto-hydrodynamic network such as theme depicted in FIG. 6,integrated into a network in which fluids are propelled by other meansthan MHD, or used as a stand-alone device. In all three implementations,MHD stirrers of the present invention may be integrated into the MHDthermal cycler of the present invention to enhance efficiency.

One application of the MHD thermal cycler is for PCR. The MHD thermalcycler has the advantage over other continuous flow devices in that thenumber of cycles may be readily adjusted in a predetermined modeaccording to the characteristics of the analyte to be amplified or in afeedback mode with the use of a sensor capable of detecting theamplification rate. Since it is not necessary to cycle the substratetemperature as is done in conventional PCRs, the MHD thermal cycler iscapable of facilitating rapid amplification of DNA.

1.-14. (canceled)
 15. A magnetohydrodynamic stirrer comprising: achamber that defines a void, the chamber having at least one sidewallthat defines a perimeter of the void, the chamber further including atop wall and an opposing bottom wall that each extend perpendicularlyfrom said at least one sidewall, wherein the top wall and bottom walldefine a top and bottom of the void, respectively; a first electrodedisposed about the perimeter of the void, proximate the at least onesidewall; a second electrode disposed on either of the top wall orbottom wall of the chamber; a third electrode disposed on either of thetop wall or bottom wall of the chamber; and a controller in operationalengagement with said electrodes, said controller, during operation,being capable of modulating the application of a potential, a current,or both between at least two of said electrodes so as to give rise toflow of a liquid within said chamber during operation of said stirrer.16. The magnetohydrodynamic stirrer of claim 15, wherein at least one ofsaid second and third electrodes extends into the void.
 17. Themagnetohydrodynamic stirrer of claim 15, wherein at least one of saidelectrodes is essentially flush with said top wall or flush with saidbottom wall.
 18. The magnetohydrodynamic stirrer of claim 15, whereinthe first electrode is disposed about an entirety of the perimeter. 19.The magnetohydrodynamic stirrer of claim 15, wherein the first electrodeis disposed about less than an entirety of the perimeter.
 20. Themagnetohydrodynamic stirrer of claim 15, wherein the first electrodeextends vertically between the top wall and the bottom wall.
 21. Themagnetohydrodynamic stirrer of claim 15, wherein said chamber comprisesan inlet and an outlet.
 22. The magnetohydrodynamic stirrer of claim 15,wherein said controller is configured to effect application of aperiodic potential, current, or both between at least two of saidelectrodes so as to give rise to chaotic advection within a liquiddisposed within said chamber during operation of said stirrer.
 23. Themagnetohydrodynamic stirrer of claim 15, wherein said controller isconfigured to effect application of a non-periodic potential, current,or both between at least two of said electrodes so as to give rise tochaotic advection within a liquid disposed within said chamber duringoperation of said stirrer.
 24. A magnetohydrodynamic stirrer comprising:a chamber that defines a void, the chamber having at least one sidewallthat defines a perimeter of the void, the chamber further including atop wall and an opposing bottom wall that each extend perpendicularlyfrom said at least one sidewall, wherein the top wall and bottom walldefine a top and bottom of the void, respectively; a first electrodehaving at least a partially annular shape spaced apart from said atleast one sidewall; a second electrode disposed on either of the topwall or bottom wall of the chamber; a third electrode disposed on eitherof the top wall or bottom wall of the chamber; and a controller inoperational engagement with said electrodes, said controller, duringoperation, being capable of the application of a potential, a current,or both between at least two of said electrodes so as to give rise toflow of a liquid within said chamber during operation of said stirrer.25. The magnetohydrodynamic stirrer of claim 24, wherein at least one ofsaid second and third electrodes is a pin that extends into the void.26. The magnetohydrodynamic stirrer of claim 24, wherein at least one ofsaid electrodes is essentially flush with said top wall or bottom wall,respectively.
 27. A method for generating Lorentz body forces in a fluidthat is at least slightly conductive within a magnetohydrodynamicstirrer, the magnetohydronamic stirrer comprising a chamber that definesa void, the chamber having at least one sidewall that defines aperimeter of the void, the chamber further including a top wall and anopposing bottom wall that each extend perpendicularly from said at leastone sidewall, wherein the top wall and bottom wall define a top andbottom of the void, respectively; the method comprising: charging thechamber with the fluid; and among (a) a first electrode disposed aboutthe perimeter of the void, proximate the at least one sidewall, (b) asecond electrode disposed on either of the top wall or bottom wall ofthe chamber, and (c) a third electrode disposed on either of the topwall or bottom wall of the chamber, applying a potential, a current, orboth between at least two of said electrodes so as to give rise to flowof a liquid within said chamber.
 28. The method of claim 27, wherein thefluid is at least partially disposed within a magnetic field orientedapproximately perpendicular both to the orientation of an axis of flowof the liquid through the chamber and to the orientation of a current orpotential applied across the electrodes.
 29. The method of claim 27wherein the applying includes implementing an activation sequence ofcurrents or potentials having specific magnitudes and polarities acrossspecific electrode pairs of the fluidic network for specific timeintervals.
 30. The method of claim 29 wherein the activation sequence isdetermined by an algorithm.
 31. The method of claim 29 wherein theactivation sequence is determined prior to its implementation in thechamber.
 32. The method of claim 29 wherein the activation sequence isdetermined with information about a state of fluid within the chamber.